Rigidity around Poisson submanifolds

• 成果类型: Article
• 署名作者: Marcut, Ioan
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-014-0118-1
• 发表日期: 2014
• 页码: 137-198
• 关键词: symplectic groupoids; THEOREM; EQUIVALENCE; MANIFOLDS; geometry

摘要

We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn's linearization theorem [2], also proving that Conn's theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to compute the Poisson moduli space of the sphere in the dual of a compact semisimple Lie algebra [17].